Enniscorthy full-back Richard Dunne scored a brace of tries for the hosts. Dundalk out-half Gearoid McDonald kicked well all afternoon and was a constant thorn in Munster's side with a penalty and a conversion the fruit of his labours.
Cashel's Michael Hickey and Clonmel's David Joyce each touched down for the visitors, with Hickey's club-mate Pat O'Connor chipping in with a penalty and Kinsale out-half Peter Murphy adding a conversion.
Leinster started brightly and after a turnover in midfield, McDonald and Barry Lynn combined nicely to put Dunne through a gap where he outpaced the cover to touch down from 60 metres out. McDonald added the conversion.
Soon after, Munster conceded a penalty inside their own half with McDonald kicking a superb 40-metre effort to give Leinster a 10-point lead.
Munster were growing in confidence and their blindside probing was working well with their back row making the hard yards, and scrum half Hickey, in particular, leading the charge with his tap and goes from penalties and free kicks.
Th visitors scored a timely try, just before half-time, as impressive number 8 Dave Hogan picked off the base of a close-in scrum and was held short but, after a couple of phases, Hickey crashed over the line for Murphy to convert and close the gap to 10-7.
Munster, with a strong wind now behind them, resumed in the second half as they finished the first and pinned Leinster back deep into their 22.
The men in red wasted some good opportunities with ball in hand and from the boot, they did, however, score a good try and penalty to lead by 15-10 with 20 minutes to go. Some excellent build-up play involving Tom Keaveny and Joe McSweeney set up a try for Joyce, with O'Connor kicking the penalty.
Leinster coach Declan O'Brien rung the changes with James Clifford, Ger Moore, Damien Broughall and Gavin Kennedy all coming into the fray to telling affect.
All of a sudden, Munster were on the back-foot with surging runs from Broughall and Brendan Kelly giving Leinster momentum.
In the closing stages, Canavan chipped through and the pacy Dunne won the race to collect the bouncing ball and touch down in the corner. Unfortunately for the defending champions, the conversion was missed.
Leinster attacked again off the restart but Munster's defence was scrambling well and they held on for a shar of the spoils, which was a fair result after a pulsating 80 minutes of rugby.
At Virginia RFC, Ulster opened their campaign with a heartening 34-23 victory over a determined Connacht side.
Ballymoney out-half Martin Irwin turned in a man-of-the-match display, helping the hosts take a 34-6 lead by the hour mark.
Connacht had tries from Tuam clubman Mike Ward and Sligo's Jordan Farrington who bagged a brace.
2009/10 IRFU JUNIOR INTERPROVINCIAL CHAMPIONSHIP:
Saturday, April 24 -
Leinster 15 Munster 15, Seapoint RFC
Ulster 34 Connacht 23, Virginia RFC
NEXT WEEK'S FIXTURES:
Saturday, May 1 -
Connacht v Leinster, Creggs RFC, 2.30pm
Munster v Ulster, Abbeyfeale RFC, 2.30pm